The control problems involved in paper-making processes can be divided into machine-directional (MD) control and cross-directional (CD) control. MD control concerns the paper properties along the machine direction and many control strategies have been reported and implemented.
CD control aims to reduce the variability of the paper property along the cross direction and to tune the dynamical property to meet the end users' specifications. The paper property is measured by a scanner mounted downstream traversing back and forth across the paper sheet; various feedback control strategies are proposed to achieve consistency of the paper profile. CD control is a challenging control problem that may involves hundreds of process actuators and hundreds or thousands of process measurements, and process models typically have a large amount of uncertainty associated with them. There are spatial and temporal aspects to this problem. The spatial aspect relates to variability of the process measurements across the sheet while the temporal aspect relates to variability of each process measurement over time.
Model predictive control (MPC), a control strategy which takes control and state constraints explicitly into consideration, has seen thousands of applications in industry, and has been recently introduced into CD control in paper-making processes with the advance of computational capability as well as the development of fast quadratic programming (QP) solvers.
In paper machine (and other flat sheet processes) CD control, one wishes to maintain the cross-directional measurement profile as close as possible to some target profile (typically a flat profile). Cross-directional model predictive control (CD-MPC) keeps measurement profiles close to target by finding sequences of actuator moves that minimize profile error from target for some period of time into the future (known as prediction horizon) according to a quadratic cost function. When the same target is used over the entire prediction horizon, the MPC controller will make aggressive actuator movements to bring the measurement profile to target as quickly as possible, unless actuator movements are somehow restrained. To restrain actuator movements to prevent undesirably aggressive movements a cost of actuator movement is included in the MPC cost function. Often this actuator movement must be heavily weighted in the cost function to prevent aggressive actuator movement in response to measurement profile deviations from target; however, this movement penalization can also make measurement responses unnecessarily slow (sluggish). A method to have faster measurement responses without undesirably aggressive control action is needed.